The Gemara in Eruvin (43) establishes that Eliyahu HaNavee (Elijah the Prophet) will come to herald the redemption on the day before the arrival of Mashiach. He will not come on Friday, the Gemara mentions, so as not to interfere with the Jews' Shabbat preparations, and therefore, by extension, Mashiach, who will arrive the day following Eliyahu's arrival, cannot come on Shabbat. The Gemara remains inconclusive regarding the issue of whether Halacha would permit Eliyahu to come on Shabbat.
This discussion in the Gemara forms the basis of a Minhag (custom) that some people have to mention Eliyahu HaNavee name many times on Motza'ei Shabbat. Some people actually recite his name 130 times – the total numerical value of Eliyahu HaNavee including the 10 letters. And some people introduce the Havdala recitation by mentioning Eliyahu three times – "Eliyahu HaNaveei, Eliyahu Ha'tishbi, Eliyahu Ha'gil'adi"). Why did these customs develop?
The reason is that Eliyahu HaNavee could not come to us on Friday, and on Shabbat, too, it is possible that his arrival would be forbidden. After Shabbat, therefore, we call out, as it were, to Eliyahu, as if to tell him, "Now you can come," that there are no longer any Halachic obstacles preventing him from coming to us.
One of the thirteen principles of Jewish faith is the belief that Mashiach can arrive "Be'chol Yom She'yavo" – any day. The Brisker Rav (Rav Yitzchak Zev Soloveitchik, Lithuania-Jeruslaem, 1889-1960) was asked how a Jew can be expected to believe that Mashiach can come today. After all, since Eliyahu did not come yesterday, Mashiach, who will come a day after Eliyahu's arrival, cannot come today.
The Brisker Rav responded that this is indeed a valid question, one which we will have to ask Eliyahu HaNavee or perhaps Mashiach himself. In the meantime, however, this technical problem must not interfere with our firm belief in the possibility of Mashiach arriving "any day," including today.